There is no character who could not be redeemed by a reboot handled correctly. Case in point, Batman. Had you asked this question after Batman & Robin, almost everyone here would have said the Dark Knight's run was finished, or at least relegated to campy tv shows. Then along came Nolan, and suddenly he's hugely popular and everyone loves him.
Lara Croft seems to be an upcoming example. If this game delivers all it promises, it will prove that there is life in the old girl yet. Even if it doesn't deliver on everything it may well show there is enough room left for more stories.
he only problem long runing characters with multiple writers ever have is that some of the writers aren't very good. All it takes is one incredible writer and everything turns around, no matter what character.
So I don't want any character to die, I want bad writers to not be allowed to write them.